Finite Group Databasebeta

← #11796045

Subgroups — #11796045

Order 1152.

660 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 660 conjugacy classes of subgroups — too many to draw. Only its 143 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64116C211yesmaximal, characteristic
2C3⋊D3×M32C212yesmaximal, complemented
3C32×#349C211yesmaximal, characteristic, complemented
4#10589419C211yesmaximal, characteristic, complemented
5#10589380C212yesmaximal, complemented
6#69119—34nomaximal
7C2×#3828C411yescharacteristic
8C2×C32×M16C2211yescharacteristic
9C22×C3⋊(C3⋊C8)C411yescharacteristic
10#64116—22no—
11#64116—22no—
12C2×#3743C411yescharacteristic
13C2×#3743C2211yescharacteristic
14C2×C8×C3⋊D3C411yescharacteristic
15C2×C8×C3⋊D3C2211yescharacteristic
16C32×M32C2212yes—
17#63639C2212yes—
18#63625—22no—
19C16×C3⋊D3—22no—
20C2×#907—34no—
21D3×M32—38no—
22C3×#349D314yescomplemented
23#4553—34no—
24#4514—38no—
25C22×C32×C4C2×C411yescharacteristic
26C2×#638C811yescharacteristic
27C2×#638C811yescharacteristic
28#3828—22no—
29#3828—22no—
30C2×C4⋊(C3⋊D3)C811yescharacteristic
31C2×C4×C3⋊D3C2×C411yescharacteristic
32C2×C4×C3⋊D3C2×C411yescharacteristic
33C2×#634C811yescharacteristic
34C32×M16—22no—
35C2×C32×C8C2×C411yescharacteristic
36C2×C32×C8C2311yescharacteristic
37C2×C3⋊(C3⋊C8)—21no—
38C2×C3⋊(C3⋊C8)—21no—
39C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
40C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
41#3743—22no—
42#3743—22no—
43C8×C3⋊D3—21no—
44C8×C3⋊D3—21no—
45C8×C3⋊D3D412yes—
46C8×C3⋊D3D412yes—
47C32×C16—22no—
48C3⋊(C3⋊C16)—22no—
49#2115—91noSylow
50C2×#235—34no—
51C2×C3×M16C2×D314yes—
52C22×C3⋊C8—34no—
53#907—68no—
54#907—68no—
55C2×ΓL(1,𝔽25)—34no—
56C2×ΓL(1,𝔽25)—34no—
57C2×D3×C8—34no—
58C2×D3×C8—34no—
59C3×M32C2×D318yes—
60#812—38no—
61#798—68no—
62D3×C16—68no—
63C23×C32C2×C811yescharacteristic
64C22×C3⋊D3C2×C811yescharacteristic
65C22×C3⋊D3C2×C811yescharacteristic
66C2×C32×C4—21no—
67C2×C32×C4—21no—
68C2×C32×C4C2×C811yescharacteristic
69C2×C32×C4C22×C411yescharacteristic
70#638—22no—
71#638—22no—
72C2×C3⋊Dic3C2×C811yescharacteristic
73C2×C3⋊Dic3C2×C811yescharacteristic
74C4⋊(C3⋊D3)—22no—
75C4×C3⋊D3—21no—
76C4×C3⋊D3—21no—
77C4×C3⋊D3C22⋊C412yes—
78C4×C3⋊D3M1612yes—
79#634—22no—
80C32×C8—21no—
81C32×C8C2×D412yes—
82C3⋊(C3⋊C8)—21no—
83C3⋊(C3⋊C8)C22⋊C411yescharacteristic
84C3⋊(C3⋊C8)C22⋊C411yescharacteristic
85C2×#131—91no—
86C2×M32—92no—
87#349—91no—
88#349—92no—
89#349C3⋊D311yescharacteristic, complemented
90C22×C3×C4C4×D314yes—
91C2×#67—34no—
92C2×#67—34no—
93#235—68no—
94#235—68no—
95C2×D12—34no—
96C2×C4×D3—34no—
97C2×C4×D3—34no—
98C2×Dic6—34no—
99C3×M16—28no—
100C2×C3×C8C4×D314yes—
101C2×C3×C8C22×D314yes—
102C2×C3⋊C8—34no—
103C2×C3⋊C8—34no—
104C2×C3⋊C8—64no—
105C2×C3⋊C8—64no—
106ΓL(1,𝔽25)—68no—
107ΓL(1,𝔽25)—68no—
108D3×C8—38no—
109D3×C8—38no—
110D3×C8—64no—
111D3×C8—64no—
112C3×C16—28no—
113C3⋊C16—68no—
114C22×C32—21no—
115C22×C32—41no—
116C22×C32C22×C811yescharacteristic
117C2×C3⋊D3—21no—
118C2×C3⋊D3—41no—
119C2×C3⋊D3—41no—
120C2×C3⋊D3C22⋊C812yes—
121C32×C4—21no—
122C32×C4C2×C22⋊C411yescharacteristic
123C32×C4C2×M1611yescharacteristic
124C3⋊Dic3—21no—
125C3⋊Dic3C22⋊C812yes—
126C2×#41—91no—
127#131—182no—
128#131—182no—
129C2×M16—91no—
130C2×M16—91no—
131C2×M16C2×C3⋊D311yescharacteristic
132C22×C8—91no—
133C22×C8—91no—
134C22×C8—91no—
135M32—92no—
136M32—182no—
137M32C2×C3⋊D312yes—
138C2×C16—182no—
139C23×C3D3×C814yes—
140C22×D3—34no—
141C22×D3—34no—
142C2×C3×C4—24no—
143C2×C3×C4—24no—
144C2×C3×C4D3×C814yes—
145C2×C3×C4C2×C4×D314yes—
146#67—68no—
147#67—68no—
148C2×Dic3—34no—
149C2×Dic3—34no—
150D12—68no—
151C4×D3—38no—
152C4×D3—38no—
153C4×D3—64no—
154C4×D3—64no—
155Dic6—68no—
156C3×C8—24no—
157C3×C8D3×D418yes—
158C3⋊C8—34no—
159C3⋊C8—34no—
160C3⋊C8—64no—
161C2×C32—21no—
162C2×C32—41no—
163C2×C32C2×C22⋊C811yescharacteristic
164C3⋊D3—22no—
165C3⋊D3—41no—
166#41—182no—
167#41—182no—
168C2×Q8—91no—
169C2×D4—91no—
170C2×D4—91no—
171C2×D4—91no—
172C22×C4—91no—
173C22×C4—91no—
174C22×C4C4×C3⋊D311yescharacteristic
175M16—22no—
176M16—182no—
177M16—182no—
178C2×C8—91no—
179C2×C8—92no—
180C2×C8—92no—
181C2×C8—91no—
182C2×C8—181no—
183C2×C8—181no—
184C2×C8—181no—
185C2×C8—181no—
186C2×C8C4×C3⋊D311yescharacteristic
187C2×C8C22×C3⋊D311yescharacteristic
188C16—22no—
189C16—182no—
190C22×C3—24no—
191C22×C3—44no—
192C22×C3C2×D3×C814yes—
193C2×D3—38no—
194C2×D3—64no—
195C2×D3—124no—
196C2×D3—124no—
197C3×C4—24no—
198C3×C4D3×C22⋊C414yes—
199C3×C4D3×M1614yes—
200Dic3—38no—
201Dic3—64no—
202C32#211511yescharacteristic, complemented, Sylow
203C23—91no—
204C23—91no—
205C23C8×C3⋊D311yescharacteristic
206Q8—182no—
207D4—182no—
208D4—182no—
209D4—182no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—91no—
213C2×C4—92no—
214C2×C4—92no—
215C2×C4—91no—
216C2×C4—181no—
217C2×C4—181no—
218C2×C4C8×C3⋊D311yescharacteristic
219C2×C4C2×C4×C3⋊D311yescharacteristic
220C8—21no—
221C8—91no—
222C8—91no—
223C8—181no—
224C8D4×C3⋊D312yes—
225C2×C3—24no—
226C2×C3—44no—
227C2×C3D3×C22⋊C814yes—
228D3—68no—
229D3—124no—
230C22—21no—
231C22—41no—
232C22—92no—
233C22—181no—
234C22—361no—
235C22—361no—
236C22C2×C8×C3⋊D311yescharacteristic
237C4—21no—
238C4—92no—
239C4—181no—
240C4C22⋊C4×C3⋊D311yescharacteristic
241C4M16×C3⋊D311yescharacteristic
242C3#6911914yescomplemented
243C2—21no—
244C2—41no—
245C2—182no—
246C2—361no—
247C2C3⋊D3×C22⋊C811yescharacteristic
subgroupG/H
centerC4C22⋊C4×C3⋊D3
commutatorC22×C32C22×C8
FrattiniC2×C8C22×C3⋊D3
FittingC32×#349C2
socleC2×C32C2×C22⋊C8
prime radicalC2×#3828C4
cosocleC2×C32×C8C23
hypercenter#349C3⋊D3
hypocenterC32#2115
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C8 ◁ #349

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C3⋊D3×M32C2semidirect
3. C32×#349C2semidirect
4. #10589419C2semidirect
5. #10589380C2semidirect
22. C3×#349D3semidirect
89. #349C3⋊D3semidirect
202. C32#2115semidirect
242. C3#69119semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#641162
C3⋊D3×M322
C32×#3492
#105894192
#105893802
#691193